It takes 12 cups of chicken broth to make soup.how much is this in quarts?

A tank with capactity 500 gal originally contains 200 gal water with 100 lbs of salt mixed into it. Water containing 1 lb of sal

prisoha [69]

Answer:

The amount of salt in the tank at any moment $t$ is

$f(t)=-\frac {4\times 10^6}{(200+t)^2}+200+t$

The concentration of salt in the tank when it is at the point of overflowing is $0.968$ .

The theoretical limiting concentration of an infinite tank is $1$ lb per gallon.

Step-by-step explanation:

Let $f(t)$ be the amount of salt in the tank at any time $t.$

Then, its time rate of change, $f'(t)$ , by (balance law).

Since three gallons of salt water runs in the tank per minute, containing $1$ lb of salt, the salt rate is

$3.1=3$

The amount of water in the tank at any time $t$ is.

$200+(3-2)t=200+t,$

Now, the outflow is $2$ gal of the solution in a minute. That is $\frac 2{200+t}$ of the total solution content in the tank, hence $\frac 2{200+t}$ of the salt salt content $f(t)$ , that is $\frac{2f(t)}{200+t}$ .

Initially, the tank contains $100$ lb of salt,

Therefore we obtain the initial condition $f(0)=100$

Thus, the model is

$f'(t)=3-\frac{2f(t)}{200+t}, f(0)=100$

$\Rightarrow f'(t)+\frac{2}{200+t}f(t)=3, f(0)=100$

$p(t)=\frac{2}{200+t} \;\;\text{and} \;\;q(t)=3$ Linear ODE.

so, an integrating factor is

$e^{\int p dt}=e^{2\int \frac{dt}{200+t}=e^{\ln(200+t)^2}=(200+t)^2$

and the general solution is

$f(t)(200+t)^2=\int q(200+t)^2 dt+c$

$\Rightarrow f(t)=\frac 1{(200+t)^2}\int 3(200+t)^2 dt+c$

$\Rightarrow f(t)=\frac c{(200+t)^2}+200+t$

Now using the initial condition and find the value of $c$ .

$100=f(0)=\frac c{(200+0)^2}+200+0\Rightarrow -100=\frac c{200^2}$

$\Rightarrow c=-4000000=-4\times 10^6$

$\Rightarrow f(t)=-\frac {4\times 10^6}{(200+t)^2}+200+t$

is the amount of salt in the tank at any moment $t.$

Initially, the tank contains $200$ gal of water and the capacity of the tank is $500$ gal. This means that there is enough place for

$500-200=300$ gal

of water in the tank at the beginning. As concluded previously, we have one new gal in the tank at every minute. hence the tank will be full in $30$ min.

Therefore, we need to calculate $f(300)$ to find the amount of salt any time prior to the moment when the solution begins to overflow.

$f(300)=-\frac{4\times 10^6}{(200+300)^2}+200+300=-16+500=484$

To find the concentration of salt at that moment, divide the amount of salt with the amount of water in the tank at that moment, which is $500$ L.

$\text{concentration at t}=300=\frac{484}{500}=0.968$

If the tank had an infinite capacity, then the concentration would be

$\lim\limits_{t \to \infty} \frac{f(t)}{200+t}= \lim\limits_{t \to \infty}\left(\frac{\frac{3\cdot 10^6}{(200+t)^2}+(200+t)}{200+t}\right)$

$= \lim\limits_{t \to \infty} \left(\frac{4\cdot 10^6}{(200+t)^3}+1\right)$

$=1$

Hence, the theoretical limiting concentration of an infinite tank is $1$ lb per gallon.

3 0

3 years ago

If 2x - 3 + 3x equals -28 what is the value of x

Paul [167]

Chapter : Linear equations

Lesson : Math of Junior High School

2x - 3 + 3x = -28

= 5x - 3 = -28

= 5x = -28 + 3

= 5x = -25

= x = -25 / 5

= x = 5

5 0

3 years ago

Read 2 more answers

Help help im so confused as per usual

Alik [6]

Answer:

Step-by-step explanation:

a. HM = 14

HN = 21

HK = 10.5

Based on intersecting chords theorem,

HK*HJ = HM*HN

10.5*HJ = 14*21 (Substitution)

HJ = 294/10.5

HJ = 28

b. VC = 7.2

VG = 12

Based on tangent-secant theorem, thus:

VD*VC = VG²

VD*7.2 = 12²

VD = 144/7.2

VD = 20

Therefore,

CD = VD - VC

CD = 20 - 7.2

CD = 12.8

6 0

3 years ago

Given a coin and a number cube which list gives the possible results?

tatiyna

Answer:

Flipping three coins: Each coin has 2 equally likely outcomes, so the sample space is 2 • 2 • 2 or 8 equally likely outcomes. Rolling a six-sided die and flipping a coin: The sample space is 6 • 2 or 12 equally likely outcomes.

...

First coin Second coin outcome

H T HT

T H TH

T T TT

Step-by-step explanation:

sorry if its wrong mate

3 0

3 years ago

4/3⋅92−29=A cylindrical-shaped water tank has a diameter of 4 feet and is 12 feet tall. Which is closest to the volume of this t

Nookie1986 [14]

Answer:

Actual volume: 150.8

Step-by-step explanation:

the equation to find the volume of a cylinder is:

V= pi (r)^2 (h)

r= radius

h= height

To get the radius, you divide the diameter by 2.

when you plug in the numbers is looks like this:

V= pi (2)^2 (12)

you'll get 150.8 ft^3

I'm not really sure which volume would be the closest, but it should be around the answer I provided

3 0

3 years ago